Career
Litex Lovech
Despodov joined Litex Lovech"s Academy at the age of 12 and progressed through the club"s youth system. On 27 November, he signed his first professional contract with Litex shortly after turning 18. Two days later he scored his second goal of the season in a 2–2 away draw against Levski Sofia in the 66th minute to clinch a point for his team
Despite the not so good start of the season 2015-2016 for Despodov, as he played only in 4 matches from 19 rounds, he become a hero in the quarterfinals of the Bulgarian Cup.
In the match against Levski Sofia, after coming on as a subtitude in the 76th minute when the match was 0:0 and Litex was down to 10 people, eventually winning the game after extra time by 3:0, with Despodov scoring 2 of the goals. On 7 February 2015, Despodov made his first appearance for Bulgaria, in a goalless draw with Romania in a non-official friendly match, coming on as a late substitute for Stanislav Manolev.